Stochastic Interacting Dynamics Financial Modelling And Statistical Analysis Of Time Series

Financial market is a complex system,and the modeling of price mechanics plays a vital important role in risk management and physical assets.The agent-based price model based on stochastic dynamic systems is one of important subjects in security market research.Approaches from the statistical physics mechanics are introduced to analyze some of these characteristics in financial markets.The use of statistical physics mechanics to investigate financial markets,called “Econophysics”,attracts many researchers.In this thesis,two new financial price model,based on the multitype rangeintensity interacting contact system and the Sierpinski gasket fractal lattice percolation with random jump,are proposed to establish the price dynamics.Then we explore and investigate the statistical properties and nonlinear complex evolution of simulated data of proposed financial dynamics.The numerical empirical study shows two financial model are reasonable to some extent.Further,we analyze the mechanism of price fluctuations in financial markets.The main work of this thesis is as follows:In Chapter 2,in an attempt to introduce novel analysis method to investigate the statistical complexity mechanics of stock markets,combining with the Black-Scholes option pricing formula,the multitype range-intensity contact(MRIC)financial model is developed based on the multitype range-intensity interacting contact system,in which the interaction and transmission of different types of investment attitudes in a stock market are simulated by viruses spreading.Another new stochastic interacting financial dynamics is proposed by Sierpinski gasket fractal lattice percolation with random jump.Sierpinski gasket is a famous example of fractals,and Sierpinski gasket lattice is a fractal-like graph which corresponds to that.In Chapter 3,we study the statistical analysis based on stochastic financial fluctuation interactive price model I.In an attempt to investigate the nonlinear complex evolution of financial dynamics,two new analyses based on random visibility graph and Lempel-Ziv complexity(LZC)are introduced to study the complex behaviors of return time series and the corresponding random sorted series.The VG method is the complex network theory,and the LZC is a non-parametric measure of complexity reflecting the rate of new pattern generation of a series.In this work,the real stock market indices are considered to be comparatively studied with the simulation data of the proposed model.Further,the numerical empirical study shows the similar complexity behaviors between the model and the real markets,the research confirms that the financial model is reasonable to some extent.In Chapter 4,we study the statistical analysis based on stochastic financial fluctuation interactive price model II.Fuzzy entropy and multiscale composite complexity synchronization are introduced to study the complexity and synchronization behaviors of returns time series,and the similar statistical methods are used to analyze the actual stock market for comparison.The results suggest that the randomness of returns series from the model increases with the increase of the parameter which indicates the frequency of unexpected events affecting the stock market within the unit time and show that the time series basically become more synchronous as the time scale increase.The empirical studies indicate that this stochastic price model is reasonable to a certain degree.In Chapter 5,we analyze the mechanism of price fluctuations in financial markets.Shocks of crude oil prices have significant effects on various economic activities.In this chapter,a novel definition of time delay based on multiscale composite complexity synchronization analysis is proposed,and it is applied to study whether stock markets have delayed reaction to crude oil markets' large volatility or not.Then,based on the multiscale time delay between crude oil markets and financial markets,the linkage synchronization and correlation relationship between crude oil markets and stock markets are measured by cross recurrence quantification analysis and deep canonical correlation analysis which is firstly utilized in this filed.